Finite Math Help

Question

E-Loan, an online lending​ service, recently offered 60​-month auto loans at 5.4% compounded monthly to applicants with good credit ratings. If you have a good credit rating and can afford monthly payments of $274​, how much can you borrow from​ E-Loan? What is the total interest you will pay for this​ loan?

Answer 1

Because the loan compounds monthly, you use the formula: 274*60 = P (1 + 0.054/12)⁶⁰.  Where 274*60 is the total you are able to pay over 60 months; 0.054/12 is the yearly interest rate 5.4% divided by 12 to get the monthly interest rate; and the exponent is 60, the number of months of compounded interest.  And then use algebra to solve for P, the principal - the amount you can borrow.  I get $12,558 rounded to the nearest dollar.  To get the total interest you'll pay, it’s 274*60 minus P, which is $3,882.